Question

For the function $f\left(x\right)=\{\begin{array}{ccc}\frac{si{n}^{2}ax}{x^2},& when& x\ne 0\\ 1,& when& x=0\end{array}$ which one is a true statement

• A. f (x) is continuous at x = 0
• B. f (x) is discontinuous at x = 0, when a $\ne \pm$ 1
  
• C. f(x) is continuous at x = a
• D. None of these

Answer 1

The correct option is B f (x) is discontinuous at x = 0, when a $\ne \pm$ 1


${lim}_{x\to 0}f\left(x\right)=\frac{si{n}^{2}ax}{\left(a{x}^2\right)}{a}^2=a^2$ and f(0) = 1
Hence f(x)is discontinuous at x = 0, when a $\ne$ 0